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Enumerating Unlabelled Embeddings of Digraphs

Published online by Cambridge University Press:  20 November 2018

Yichao Chen ,
Xiaojian Gao  and
Yuanqiu Huang
Yichao Chen
Affiliation:
Department of Mathematics, Hunan University, 410082 Changsha, China e-mail: ycchen@hnu.edu.cn
Xiaojian Gao
Affiliation:
Department of Mathematics, Hunan University, 410082 Changsha, China e-mail: s12061017@hnu.edu.cn
Yuanqiu Huang
Affiliation:
Department of Mathematics, Normal University of Hunan, 410081 Changsha, China e-mail: hyqq@hunnu.edu.cn
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Abstract

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A 2-cell embedding of an Eulerian digraph $D$ into a closed surface is said to be directed if the boundary of each face is a directed closed walk in $D$. In this paper, a method is developed with the purpose of enumerating unlabelled embeddings for an Eulerian digraph. As an application, we obtain explicit formulas for the number of unlabelled embeddings of directed bouquets of cycles ${{B}_{n}}$, directed dipoles $O{{D}_{2n}}$ and for a class of regular tournaments ${{T}_{2n+1}}$.

Keywords

05C10Eulerian digraphdirected embeddingunlabelled embedding
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 55 - 69
Copyright
Copyright © Canadian Mathematical Society 2018

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